Question

In how many elements the last electron will have the following set of quantum numbers, \(n=3\) and \(l=1 ?\) (a) 2 (b) 8 (c) 6 (d) 10

Short answer

(c) 6

Step-by-step solution

Understanding Quantum Numbers

The principal quantum number (n) indicates the energy level and size of the orbital. For n=3, we have the third energy level. The azimuthal (or angular momentum) quantum number (l) defines the shape of the orbital. For l=1, the shape is a p-orbital which has three p-orbitals (px, py, pz) at any energy level.

Determining the Maximum Number of Electrons

Each p-orbital can hold a maximum of 2 electrons (one with spin up and one with spin down). Since there are 3 p-orbitals for l=1, the total number of electrons that can be accommodated is 3 orbitals * 2 electrons/orbital = 6 electrons.

Identifying the Correct Answer

Since we've determined that the maximum number of electrons in the n=3, l=1 subshell is 6, the correct answer is (c) 6.

Key concepts

Principal Quantum Number

The principal quantum number, denoted as 'n', is crucial in understanding the structure of an atom's electron shell. It defines the energy level of an electron and its likely distance from the nucleus. As 'n' increases, the energy and size of the orbitals also increase, meaning the electron is likely to be found further away from the nucleus. For instance, when considering the quantum numbers in our example, with n = 3, electrons are located in the third principal shell, which is more energized and expansive than the first two inner shells.

This shell can hold more electrons than the innermost ones because as the value of 'n' rises, the possible number of subshells and corresponding orbitals within each shell increases, allowing for a larger electron capacity.

Azimuthal Quantum Number

The azimuthal quantum number, commonly referred to as the 'angular momentum quantum number' or 'l', details the subshell, or the shape, of an orbital within a principal energy level. Its value ranges from 0 to n-1, where each number corresponds to a different type of orbital:

• l = 0 (s-orbital)
• l = 1 (p-orbital)
• l = 2 (d-orbital)
• l = 3 (f-orbital)

For example, when we have l = 1, as in the given problem, the electrons are in a p-type orbital. This orbital type is characterized by its dumbbell shape and is oriented in three-dimensional space, often denoted as px, py, and pz. Each of these p-orbitals can accommodate two electrons, and they are significant in determining the chemical bonding and properties of an element.

p-Orbitals

As p-orbitals correspond to the azimuthal quantum number of l = 1, they are one of the various types of orbitals within an atom's electron configuration. P-orbitals are crucial for visualizing how electrons are distributed around an atom's nucleus and represent regions in space where these electrons have a higher probability of being detected. A complete set of p-orbitals at a given energy level consists of three orbitals: px, py, and pz, representing the three spatial axes.

Each p-orbital can hold two electrons, implying a total of six electrons for all three. The p-orbitals exhibit a dumbbell shape and are pivotal when considering atomic orbitals involved in the formation of chemical bonds and the geometry they influence in molecules.

Electron Configuration

Electron configuration is the arrangement of electrons in an atom's orbitals and is dictated by a well-defined set of rules based on quantum numbers. Simply put, it's the 'address' of an electron within an atom, specifying its position in terms of the principal (n), azimuthal (l), magnetic (m), and spin (s) quantum numbers. The order in which electrons fill these orbitals follows the Pauli exclusion principle and Hund's rule, leading to the lowest possible energy configuration of the atom.

Understanding electron configuration is fundamental for predicting chemical properties and behaviors such as the type of bonds an atom might form, its reactivity with other atoms, and its role within chemical reactions. For the problem at hand, the electron configuration aspect helps us to visualize the specific occupancy for the n=3, l=1 electrons within the p-orbitals.

Chemical Education

The field of chemical education bridges the gap between complex scientific concepts and effective learning strategies for students. It involves creating tools, like step-by-step solutions to textbook problems, developing curricula that help students to logically and visually follow the path of scientific reasoning. An approach that breaks down topics like quantum numbers into digestible parts and practical examples enables learners to construct a meaningful understanding of chemistry's fundamental principles.

Teaching tools may include interactive simulations, visual aids such as orbital diagrams, and carefully crafted exercises that lead students through the often intricate landscape of chemical knowledge. The goal is for students to not only memorize facts but also to develop problem-solving skills and an intuitive grasp of how chemical phenomena occur and can be predicted or explained in the context of quantum mechanics and other theories.